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3 years ago

two consecutive even integers have a sum of 254. write the equation that will solve for the two integers.

Mathematics

1 answer:

kobusy [5.1K]3 years ago

5 0

Answer: 126 and 128

Step-by-step explanation: In this problem have two consecutive even integers whose sum is 254.

Consecutive even integers can be represented as followed.

X ⇒ first even integer

X + 2 ⇒ second even integer

Since the sum of these is 254, our equation reads X + X + 2 = 254.

We can simplify on the left side of the equation to get 2x + 2 = 254.

Now, we subtract 2 from both sides of the equation to get 2x = 252.

Lastly, we will divide both sides of the equation by 2 in order to isolate x. On the left side, the 2's cancel out and on the right, 252 divided by 2 is 126.

If our first integer is 126, our next consecutive even integer will be 126 + 128 which simplifies to 254.

Therefore, our two consecutive even integers are 126 and 128.

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Read 2 more answers

A group of 100 students took a quiz. Their average score was 76 points. If the average score for the boys was 80 points and the

sveta [45]

Answer:

The number of girls participated in quiz is 40 .

Step-by-step explanation:

Given as :

Total number of students took quiz = 100

Average score of 100 students = 76 points

The Average score of boys = 80 points

The Average score of girls = 70 points

Let The number of boys participated in quiz = b

Let The number of girls participate in quiz = g

Now, According to question'

Total number of students took quiz = number of boys participated in quiz + number of girls participated in quiz

Or, b + g = 100 ........A

Again

∵ Average score of 100 students = 76 points

∴ Total score of 100 students = 76 × 100 = 7600

So, Average score of boys × number of boys participated + Average score of girls × number of girls participated = Total score of 100 students

Or, b × 80 + g × 70 = 7600

Or, 80 b + 70 g = 7600 .........B

Now, Solving equation A and B

(80 b + 70 g ) - 70 ×( b + g ) = 7600 - 70 × 100

I.e (80 b - 70 b) + (70 g - 70 g) = 7600 - 7000

Or, 10 b + 0 = 600

∴ b = $\dfrac{600}{10}$

i.e b = 60

So, The number of boys participated in quiz = b = 60

Put the value of b into eq A

∵ b + g = 100

So, g = 100 - b

Or, g = 100 - 60

i.e g = 40

So, The number of girls participated in quiz = g = 40

Hence, The number of girls participated in quiz is 40 . Answer

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3 years ago

The radius of a wheel is 21m.how much distance will it covers when it rotates 5 times?

mrs_skeptik [129]

Answer:

Distance = 660 meters

Step-by-step explanation:

Given the following data;

Radius, r = 21 m

Number of revolutions = 5 times

To find the distance covered;

The distance covered in one revolution is given by the circumference of a circle.

Mathematically, circumfeence of a circle is equal to;

C = 2πr

Substituting into the formula, we have;

C = 2 * 22/7 * 21

C = 44 * 3

C = 132 meters

Next, we find the distance covered;

Distance = Circumference * Number of revolutions

Distance = 132 * 5

Distance = 660 meters

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2 years ago

3 Ramón makes nectar for a hummingbird feeder by mixing 8 cups of water with 2 cups of sugar. Tiffany makes nectar by mixing 9 c

Butoxors [25]

Answer:

Tiffany's nectar is more sugary

Step-by-step explanation:

Given

Ramon:

$Water = 8\ cups$

$Sugar = 2\ cups$

Tiffany

$Water = 9\ cups$

$Sugar = 3\ cups$

Required

The nectar with more sugar

To do this, we simply calculate the fraction of sugar in both nectar.

This is calculated as:

$Fraction = \frac{Sugar}{Sugar + Water}$

For Ramon:

$Fraction = \frac{2}{8 + 2}$

$Fraction = \frac{2}{10} = 0.20$

For Tiffany

$Fraction = \frac{3}{3 + 9}$

$Fraction = \frac{3}{12} = 0.25$

From the calculations above:

$0.25 > 0.20$

Hence: Tiffany's nectar is more sugary

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3 years ago